This is a fast and compact guide: To get a good and solid overview in little time.

If you are looking for a long in-depth guide, i can recommend:
http://www.heroesfire.com/hots/guide/arthas-quot-hail-to-the-king-baby-quot-updated-34


All talents except level 10 and 13 remain the same nearly every game because they just support Arthas fitting into the tank role of the current meta.
The optional talents on level 10 and 13 are explained below cause you will have to decide for them differently depending on your current game.

I also added a "Arthas + Jaina (Combo Build)", if you want to get maximum value out of that combo. But if you not play exactly that combination you should stick to the "Soak Tank (Main Build)".

Lvl 10 Talents:

When to go for "Army Of The Dead" and when to go for "Summon Sindragosa".

Basically Army of the Dead is never a bad option, it gives you more healing in the fight and the ghouls deal a decent ammount of damage. You won't make a mistake by taking this as your level 10 talent most of the time.

The big question is when to choose Summon Sindragosa. I will try to explain the factors which should lead you into making the right descision.

In general Sindragosa is good on maps where you have to protect a certain spot like the pirate or a temple, you can ult across the contested spot and it will either hit multiple targets or zone them away.
Also this talent is good when you are the only engage your team has or you have heroes like Jaina on your team that profit from enemies who get frozen or stuck.
The effect that it stops towers and minions from attacking is nice and can be used in some rare situations but it should not be a priority to concider when choosing your level 10 talent.

The negative thing about this talent is that you give away the insane self-heal Arthas has when he sacrafizes the ghouls of his Dead Army. When your healer has no hard burst heal or your team is lacking in heal you could lose the game due to you not having enough sustain to soak the enemy damage long enough.

Basically you have to decide every game if you need the self-heal/engage/protection of an area and think about the pros/cons for that game to make your choice. But generally the Army Of The Dead would be the safer choice.

Lvl 13 Talents:

I list the 3 good talents you should choose from and a short explanation when to do so. Spell Shield/Relentless can be taken most of the time when you are the only tank on your team but there are some situations where the other talents might be a better choice:

Spell Shield: You getting bursted too hard or the enemy team has a at least 2 caster heroes

Relentless: Enemies have a lot of CC, especially the Brightwing polymorph is crucial for arthas

Trail of Frost: Your team needs more CC or needs to root multiple targets at the same time